I did a similar job for a buddy a while back, but it was a lot worse and all 3 walls had to be re-boarded cos the plaster-board was rotten.
To rectify the tray issue, but to avoid extra expense, I sat the tray on several cut of pieces of fence post, which kept the height but removed as much flex as we could because the edge of the tray sat on something solid all the way around. 2 years on and its all good still....